The generator matrix

 1  0  1  1  1  X  1  1 X+2  1  2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X
 0  1  1  2 X+1  1  X X+3  1 X+2  1 X+3 X+3  3  1  1  2  0 X+2 X+2  X X+2  0  2  3  2  0 X+1 X+2
 0  0  X X+2  2 X+2  X X+2  0  0  X  2  X  0  2 X+2  0 X+2 X+2  2  0  X  2  X X+2  2  X  0  X

generates a code of length 29 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+56x^27+41x^28+88x^29+8x^30+40x^31+12x^32+8x^33+1x^36+1x^48

The gray image is a code over GF(2) with n=116, k=8 and d=54.
This code was found by Heurico 1.16 in 0.00724 seconds.